Free Printable 8th Grade STAAR/Benchmark 03

1.

Trapezoid WKRP was translated 4 units to the left and 5 units up on a coordinate grid to create trapezoid W'K'R'P'. Which rule describes this transformation?

a)

$\left(x,\ y\right)\ \rightarrow\ \left(x\ -\ 4,\ y\ +\ 5\right)$

b)

$\left(x,\ y\right)\ \rightarrow\ \left(x\ +\ 4,\ y\ -\ 5\right)$

2.

Triangle XYZ is rotated 90° clockwise about the origin to form triangle X'Y'Z'. Which statement is true?

a)

The area of triangle XYZ is equal to the area of triangle X'Y′Z'

b)

The area of triangle XYZ is more than the area of triangle X'Y′Z'

c)

The area of triangle XYZ is less than the area of triangle X'Y′Z'

3.

A transformation is applied to a figure to create a new figure on a coordinate grid. Which transformation does NOT preserve congruence?

a)

A dilation by a scale factor of 1.5

b)

A reflection across the y-axis, or x-axis

c)

A translation of 125 units down

4.

A figure was transformed on a coordinate grid using the rule;

(x, y) → (−x, -y). Which of the following describes this transformation?

a)

A 180° clockwise rotation about the origin

b)

A reflection across the x-axis

c)

A reflection across the y-axis

5.

Triangle ABC was transformed to create triangle A'B'C'. Which rule best describes this transformation?

a)

$\left(x,\ y\right)\ \rightarrow\ \left(x,\ y\ -\ 7\right)$

b)

$\left(x,\ y\right)\ \rightarrow\ \left(x\ -\ 7,\ y\right)$

6.

Quadrilateral KMPT is dilated by a scale factor of $\frac{3}{4}$ to create quadrilateral K'M'P′T′. The perimeter of quadrilateral KMPT is x units. What is the perimeter in units of quadrilateral K'M′P′T′?

a)

$\frac{3}{4}x\ units$

b)

$\frac{4}{3}x\ units$

7.

Quadrilateral PQRS was translated 5 units to the right and 3 units up to create quadrilateral P'Q'R'S'. Which rule describes this transformation?

a)

$\left(x,\ y\right)\ \rightarrow\ \left(x\ +\ 5,\ y\ +\ 3\right)$

b)

$\left(x,\ y\right)\ \rightarrow\ \left(x-5,\ y\ -\ 3\right)$

8.

Trapezoid PQRS is rotated 180° about the origin to form trapezoid P'Q'R'S'. Which statement is true?

a)

The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid P'Q'R'S'.

b)

The angle measures of trapezoid PQRS will NOT be equal to the corresponding angle measures of trapezoid P'Q'R'S'.

9.

Pentagon VWXYZ is shown on the coordinate grid. A student reflected pentagon VWXYZ across the x-axis to create pentagon V'W'X'Y'Z'. Which rule describes this transformation?

a)

$\left(x,\ y\right)\ \rightarrow\ \left(x,\ -y\right)$

b)

$\left(x,\ y\right)\rightarrow\ \left(-x,\ y\right)$

10.

Triangle RST is translated 6 units to the left and 4 units up to create triangle R'S′T′. Which rule best describes this transformation?

a)

$\left(x,\ y\right)\ \rightarrow\ \left(x\ -6,\ y\ +\ 4\right)$

b)

$\left(x,\ y\right)\ \rightarrow\ \left(x\ +\ 6,\ y\ -\ 4\right)$

11.

Triangle TRW is shown on the coordinate grid. Triangle TRW will be dilated by a scale factor of 'n' with the origin as the center of dilation to create triangle T'R'W'. Which ordered pair best represents the location of point R′ ?

a)

$\left(-3n,\ -5n\right)$

b)

$\left(-\frac{5}{n},\ \frac{3}{n}\right)$

12.

Polygon LMNPQR is shown on the coordinate grid and models the shape of a garden in a park. Polygon LMNPQR will be dilated with the origin as the center of dilation to create polygon L'M′N′P′Q′R′. The vertex Q′ will be located at (21, 7). Which rule best represents the dilation?

a)

$\left(x,\ y\right)\ \rightarrow\ \left(\frac{7}{2}x,\ \frac{7}{2}y\right)$

b)

$\left(x,\ y\right)\ \rightarrow\ \left(\frac{1}{7}x,\ \frac{1}{7}y\right)$

13.

Triangle ABC and triangle DEF are similar. Which proportion must be true?

a)

$\frac{4}{6}=\frac{x}{7}$

b)

$\frac{4}{6}=\frac{7}{x}$

14.

Figure I and Figure II are similar figures. Which proportion must be true?

a)

$\frac{ST}{EF}=\frac{WR}{CD}$

b)

$\frac{ED}{VU}=\frac{RW}{ST}$

15.

A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?

a)

$\left(x,\ y\right)\ \rightarrow\ \left(0.9x,\ 0.9y\right)$

b)

$\left(x,\ y\right)\ \rightarrow\ \left(2x,\ 2y\right)$

c)

$\left(x,\ y\right)\ \rightarrow\ \left(\frac{7}{5}x,\ \frac{7}{5}y\right)$

16.

A polygon is graphed on a coordinate grid with (x, y) representing the location of a certain point on the polygon. The polygon is transformed using the rule (x, y) $\rightarrow$ (ax, ay). Which statement must be true?

a)

If 'a' is between 0 and 1, the image of the polygon is smaller than the polygon.

b)

If 'a' is between 0 and 1, the image of the polygon is bigger than the polygon.

17.

Triangle JKL is dilated with the origin as the center of dilation to create triangle J'K′L'. Which rule best represents the dilation that has been applied to triangle JKL to create triangle J'K'L'?

a)

$\left(x,\ y\right)\ \rightarrow\ \left(\frac{7}{4}x,\ \frac{7}{4}y\right)$

b)

$\left(x,\ y\right)\ \rightarrow\ \left(\frac{4}{7}x,\ \frac{4}{7}y\right)$

18.

A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation. If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?

a)

$\left(0.4x,\ 0.4y\right)$

b)

(20x, 20y)

19.

Figure I and Figure II are similar quadrilaterals. Which proportion must be true?

a)

$\frac{3.2}{2}=\frac{a}{8}$

b)

$\frac{3.2}{2}=\frac{8}{a}$

20.

Triangle KLM and triangle PRS are similar right triangles. Which proportion can be used to show that the slope of is equal to the slope of ?

a)

$\frac{KL}{LM}=\frac{PR}{RS}$

b)

$\frac{KL}{LM}=\frac{RP}{SP}$

21.

At a restaurant 600 customers were served during a 10-hour period of time. Which graph has a slope that best represents the number of customers that were served per hour at this restaurant?

a)

b)

22.

A linear function is represented on the coordinate grid. What is the y-intercept of the graph of this function?

a)

5

b)

6

c)

8

d)

0

23.

A survey of customers at a restaurant revealed that 7 out of 10 customers preferred the restaurant’s new spaghetti sauce. Which graph shows the relationship between y, the number of customers who preferred the new spaghetti sauce, and x, the total number of customers?

a)

b)

24.

The graph of a linear function is shown on the coordinate grid. What is the slope of the graph of this function in decimal form?

a)

$\frac{1}{2}$

b)

0.5

c)

$\frac{1}{4}$

d)

0.25

25.

The cost of 6 pencils at a store is 30 cents. Each pencil has the same cost. Which graph has a slope that best represents the cost of each pencil at this store?

a)

b)

26.

A hot-air balloon is released at ground level, and it rises into the air at a constant rate. After 5 seconds the height of the balloon is 20 feet. The balloon continues to rise at the same rate. Which table shows the relationship between the time in seconds, x, and the height of the balloon in feet, y?

a)

b)

27.

Rudolfo has 15 toys in his toy box, and he adds 2 new toys every month. Based on this information, which representation best shows this relationship between the number of toys Rudolfo has in his toy box, y, and the number of months that have passed, x?

a)

b)

c)

28.

The ticket sales for a concert started at 4:00 P.M. The table shows the linear relationship between the number of tickets remaining and the number of hours since 4:00 P.M. Which function can be used to find y, the number of tickets remaining x hours since 4:00 P.M.?

a)

$y\ =\ -3000x\ +\ 15000$

b)

$y\ =\ -15000x\ +\ 3000$

29.

Oscar buys his lunch in the school cafeteria. The cost of 15 school lunches is $33.75. Which graph has a slope that best represents the average cost of the lunches in dollars per lunch?

a)

b)

30.

Triangle PSV is shown on the coordinate grid. The coordinates of each vertex of the triangle are integers. What is the slope of PV?

a)

-4

b)

4

c)

5

d)

$\frac{1}{4}$

31.

Triangle HJK and triangle PMK are similar right triangles. The coordinates of all the vertices are integers. Which statement is true about the slope of HK and the slope of PK?

a)

The slope of HK is equal to the slope of PK, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for HK as it is for PK.

b)

The slope of HK is not equal to the slope of PK, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is different for HK as it is for PK.

c)

The slope of HK is less than the slope of PK, because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is not the same for HK as it is for PK.

32.

A bottle contains 30 fluid ounces of orange juice and 18 fluid ounces of pineapple juice. Which graph has a slope that best represents the ratio of orange juice to pineapple juice in this bottle?

a)

b)

33.

The table shows the linear relationship between the number of hours Francis worked, x, and the amount of money Francis earned, y. Based on the table, how much did Francis earn per hour?

a)

$14 per hour

b)

$15 per hour

c)

$12 per hour

34.

A gym charges a membership fee plus an additional fee per yoga class. The table shows the linear relationship between the number of yoga classes taken and the total cost including the membership fee. Which statement is true?

a)

The additional fee per yoga class is $3.75.

b)

The additional fee per yoga class is $4.75.

35.

Joseph ran a 6-mile race in 48 minutes. Which graph has a slope that best represents Joseph’s average rate of speed during the race?

a)

b)

36.

A company sells bottles of vitamin capsules. The graph and table show the linear relationship between the cost per capsule in cents and the number of bottles ordered. What is the slope of the line that models this situation?

a)

-5

b)

-3

c)

2

d)

0

37.

An oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours. Which graph has a slope that best represents this rate?

a)

b)

c)

38.

Which table represents a non-proportional relationship between x and y?

a)

b)

39.

A water tank currently contains 275 gallons of water. The amount of water in the tank will decrease at a constant rate of 15 gallons per week. Which function can be used to find 't', the total number of gallons of water in the tank after 'w' weeks?

a)

t = -15w + 275

b)

t = 15w - 275

40.

A teacher bought markers at a cost of $3 per set. The teacher had a $2-off coupon to use toward the total cost of the markers bought. Which table shows the relationship between x, the number of sets of markers bought by the teacher, and y, the total cost of the markers?

a)

b)

41.

The graph shows a relationship between x and y. Which statement is true?

a)

The graph shows a non-proportional relationship because the graph does not contain the origin.

b)

The graph shows a non-proportional relationship because the graph pass through the origin.

42.

A coach is ordering shirts for a team.

$\rightarrow$ The coach pays a one-time fee of $24.

$\rightarrow$ The coach also pays $8 for each shirt ordered.

Which function can be used to find c, the total amount the coach pays in dollars when k shirts are ordered?

a)

y = 8k + 24

b)

y = 24k + 8

43.

The graph shows the relationship between the number of gallons of fuel remaining in the tank of a semitruck and the number of miles traveled by the semitruck. Which function can be used to find y, the number of gallons of fuel remaining in the tank of the semitruck after it has traveled x miles?

a)

$y\ =\ -\frac{1}{10}x+240$

b)

$y\ =\ -240x\ +\ \frac{1}{10}$

44.

Which graph appears to show a proportional relationship between x and y?

a)

b)

c)

45.

On a map scale, 2 inches represents 60 miles. Which graph best shows the relationship between x, the number of inches on the map, and y, the actual distance in miles?

1 inch = 30 miles

a)

b)

46.

Which function is best represented by this graph?

a)

$y\ =\ \frac{1}{4}x\ -\ 2$

b)

$y\ =\ \frac{1}{2}x\ -\ 2$

c)

$y\ =\ -\frac{1}{4}x\ -\ 2$

8th Grade STAAR/Benchmark 03

Total questions: 46

Worksheet time: 23mins

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